Old English leohtlice "so as not to be heavy" (of material things, but also of sleep, blows, etc.), from light (adj.1) + -ly (2). Similar formation in Old Frisian lichtelik, Old High German lihtlihho, German leichtlich, Old Norse lettlega (see light (adj.1)). Meaning "frivolously, indifferently" is from early 13c. (compare Old English leohtmodnes "frivolity").
one cannot say such things lightly
she kissed him lightly on the forehead
we eat lightly in the morning
he took it lightly
apply paint lightly
her speech is only lightly accented
light-headed
light-hearted
lighthouse
lighting
lightless
lightly
lightness
lightning
lights
lightweight
light-year